Question
Factorize of the following expressions:
$ a b\left(x^2+1\right)+x\left(a^2+b^2\right) $
$ a b\left(x^2+1\right)+x\left(a^2+b^2\right) $
✓
Answer
$ a b\left(x^2+1\right)+x\left(a^2+b^2\right)=a b x^2+a b+a^2 x+b^2 x $
$ =\left(a b x^2+a^2 x\right)+\left(b^2 x+a b\right) $
$= ax(bx + a) + b(bx + a) = (ax + b)(bx + a) [$taking $(bx + a)$ as the common facotor$]$
$ =\left(a b x^2+a^2 x\right)+\left(b^2 x+a b\right) $
$= ax(bx + a) + b(bx + a) = (ax + b)(bx + a) [$taking $(bx + a)$ as the common facotor$]$
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